# Lesson 9

Solving Problems about Proportional Relationships

### Problem 1

For each situation, explain whether you think the relationship is proportional or not. Explain your reasoning.

- The weight of a stack of standard 8.5x11 copier paper vs. number of sheets of paper.
- The weight of a stack of different-sized books vs. the number of books in the stack.

### Solution

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### Problem 2

Every package of a certain toy also includes 2 batteries.

- Are the number of toys and number of batteries in a proportional relationship? If so, what are the two constants of proportionality? If not, explain your reasoning.
- Use \(t\) for the number of toys and \(b\) for the number of batteries to write two equations relating the two variables.
\(b = \)

\(t = \)

### Solution

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### Problem 3

Lin and her brother were born on the same date in different years. Lin was 5 years old when her brother was 2.

- Find their ages in different years by filling in the table.
Lin's age Her brother's age 5 2 6 15 25 - Is there a proportional relationship between Lin’s age and her brother’s age? Explain your reasoning.

### Solution

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### Problem 4

A student argues that \(y=\frac{x}{9}\) does not represent a proportional relationship between \(x\) and \(y\) because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student?

### Solution

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(From Unit 2, Lesson 8.)### Problem 5

Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select **all** of the following that are side lengths of Quadrilateral B.

5

6

7

8

9

### Solution

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(From Unit 1, Lesson 3.)